This is an important concept for the soloist to grasp, but it's actually a bit hard to define or explain. Here's the Wikipedia definition:
A musical phrase... is a unit of musical meter that has a complete musical sense of its own... built from figures, motifs, and cells and combining to form melodies, periods and larger sections... or the length in which a singer or instrumentalist can play in one breath.
That's a lot to read. Don't worry about any words in there you didn't understand, because unless you're writing a symphony or analyzing Mozart you don't really need to know them. But it's good to look at some of the stuff there because it can really help us out.
Speaking of Mozart, let's check out one of his melodies that everyone knows, broken down into two phrases:
Phrase 1 - Eine Kleine Nachtmusik - Mozart
Phrase 2 - Eine Kleine Nachtmusik - Mozart
Do you hear how each set of four measures is a complete musical thought? Both phrases stand alone and yet go together so well to form a melody.
Have you ever heard someone say, "Make it talk, son" when referring to a guitar solo? That's exactly what you should be doing! Soloing and speaking are very similar. You can think of the parallels as follows:
For now, let's focus on sentences. A sentence, like a musical phrase, makes sense by itself - it's a complete thought. A sentence can end with different punctuation, which can drastically change the meaning. It can be slow or fast, long or short, loud or soft. A sentence can convey emotion. Finally, a sentence has a rhythm to it when you read it, and certain syllables that are accented.
I realize that's a lot to think about. To put this into practice, try creating a solo that really speaks. Make up or read a sentence and get it stuck in your head. Then try to re-create that sentence using your guitar. Literally make your guitar talk! Don't forget to pause after each musical idea just like you would pause after each sentence when you speak.
Here's a fun example of a soloist (Sam) making sentences on his instrument. I realize he's just imitating the singer, but it's a great way to illustrate phrasing:
Pennies From Heaven - Louis Prima
And here's Gilmour making his guitar sing. This section is two big phrases:
On the Turning Away - Pink Floyd
Finally, here's Peter Frampton with a clip from a recent version of the famous song "Do You Feel Like We Do". Frampton is literally using vocal phrases to solo!
When you are constructing a solo, think of it like a paragraph. A paragraph has a unifying theme to it. Each sentence stands on its own but relates to the overall topic. There's a lot of flexibility here, just like there are lots of ways to speak.
Above all, speak through your solos and make your guitar talk!