Hope you like similes, because they're going to keep coming! Each of the next three stanzas is built around a poetic comparison.
In this case, the bird is compared to a princess in a tower. (All we can see is Disney's Sleeping Beauty. Guess that's what watching too many cartoons when you're little will do to you.)
Either way, thought this comparison the bird is elevated—both in terms of being "high-born" and in a literal sense!
Soothing her love-laden Soul in secret hour
You pretty much know the story here. The Princess is in love, and needs to be comforted. There are plenty of intense feelings in this poem, that's for sure.
There's plenty of alliteration, too: "love-laden," "soul in secret." Fun!
With music sweet as love, which overflows her bower
The princess is soothing herself with music in her private room ("bower"). We imagine her singing to herself, just like the skylark, even though the speaker doesn't say exactly what kind of music we're dealing with here.
By now you're probably getting used to the themes here. Music and feeling and poetry all blend together. So it's not too surprising to find the skylark connected with beautiful princesses and sweet love songs.