But first thing's first. How did Liverpool become a hotbed for music rooted in a British interpretation of African American rhythm and blues (because that's exactly what Merseybeat was)? Being a port city, Liverpool has been a culturally rich city throughout its 800-year existence. The cooperation of the US and the UK during World War II brought thousands of American soldiers and sailors into the city; they brought their music with them, beginning the cross-pollination of sounds that launched the British adventure into American music. Ringo Starr later remembered, "I'd go to parties and [the navy guys] would be putting on Hank Williams, Hank Snow, and all those country acts" The rest of the Fab Four had similar experiences, each of them bringing to the table a different set of American influences—George Harrison loved folk and bluegrass, while Paul McCartney and John Lennon were both devotees of early rock 'n' roll acts like Chuck Berry.
Being the adventurous Brits they were, the Beatles led the way in combining these sounds to construct a distinct new sound out of all these mostly-American influences. Merseybeat was more dangerous than the skiffle and doo-wop that came before it, but nonetheless remained more fun and catchy than edgy. Merseybeat doesn't get any better than "I Want To Hold Your Hand," which features a strong backbeat, vocal harmonies, and conventional (perhaps bordering on homogeneous) pop song structure. That said, if you know anything about The Beatles, you know that it was their sometimes-subtle variation of general musical themes that made them so special; in that vein, the very apotheosis of Meserybeat, "I Want To Hold Your Hand," toyed with the essential characteristics of the style.
The beat of the song is a good example of this. According to Pam Hurry, Mark Philips, and Mark Richards, authors of Heinemann Advanced Music, Merseybeat was characterized by its emphasis of every beat in a measure, as opposed to the backbeat emphasis in American rock n' roll. But that glosses over all the little details and doesn't really tell you much about the music itself. It may indeed be true that every beat is emphasized in Merseybeat, but The Beatles made that sound more interesting. If you listen to "I Want To Hold Your Hand" you'll indeed find that every beat has an emphasis in at least one section of the song—but not every beat is emphasized by the same instrumentation. The vocals emphasize the downbeat (the first beat in the measure). Then there's the syncopated clapping, and opposed to that, you get the rock 'n' roll sound from Ringo Starr's backbeat on the drums. (A backbeat is a beat that emphasizes the even notes in a measure.) Because we count the measures in this song in four beats, this means the second and fourth beats are emphasized. The key to figuring out which beats the drummer emphasizes usually involves listening for the snap of the snare drum.
Spitz also mentions the "full, rich [vocal] harmonies" and "ensemble musicianship" as highlights of the song. Unlike the rock n' roll groups of America, in which the lead-guitar showman was beginning to emerge, here no one is playing over one another or taking the reigns. In every sense, The Beatles are a group of four all playing together, whereas you would associate some groups with a single player or two. In that vein the vocals too are tightly knit; Lennon and McCartney sing at the same time, and you could say that either both or neither are singing "lead." They sing at the same volume and, when the do create harmonies, those harmonies are close to one another. Vocal harmonies are used much like strumming strings on a guitar together, to produce chords or interesting intervals. McCartney and Lennon sing either in unison or in fifth or third intervals to each other, filling out basic chord sounds with their vocals. Typically vocal harmonies are sung at third intervals (you don't need to know what that means) but McCartney and Lennon favor singing at a different interval (the fifth), which makes their harmony somewhat unique. The pair uses harmony quite elegantly and sparingly. Harmony is used to emphasize exciting parts of the song as it builds. Notice, for example how during the second bridge section of the song ("And when I touch you..." etc.) Lennon and McCartney sing harmony instead of in unison as they build to the end of the song.
The song uses popular chord progressions. The study of chord progressions is beyond a lot of popular musicians, but it is an interesting way of looking at how pop music functions. Essentially, we want to know how to get from one cool riff to another without sounding bad. The bridge section provides an interesting case of this. It is comprised of overlapping II-V-Is. If you're not already trained in music theory, this will take a little bit of explanation. Music theorists like to use Roman numeral notation to describe the chord relations in a song relative to a key. The II numeral says that the chord is the second in that key. A II-V-I in music is a turnaround used to get a song from one place to another—making its use in a bridge (a section in music that, like the structure, gets you from one place to another) quite fitting.
Understanding why "getting somewhere" is necessary in a song requires only a little common sense. The same bit of music is only interesting for so long. That's why pop songs typically only last for three minutes or so. Often a song will add a bridge section as a means of changing things up so the song can remain interesting. It is just common pop music practice.
So, in the interest of staying interesting, "I Want To Hold Your Hand" jumps to a D minor 7 chord—something we haven't heard in the song yet, in the bridge. To fit in with the rest of the song, there has to be some pretty way of getting back to status quo in the song. That II-V-I gets us there. The end of the bridge section is a recapitulation of the song's intro, which begins on C. Put into chords, the II-V-I of this song is D minor 7 (Dm7)-G-C. That final C Major can jump into the chord progression of the intro—and thus the verse—without sounding weird. Ahh, resolution!