My candidate for best ever blues solo is this:
BUDDY GUY - FIRST TIME I MET THE BLUES - LIVE 1970 - YouTube
It starts out with four choruses of just guitar, starting with lots of space between phrases, and building quite slowly - pulling the suspense and tension this way and that, using mostly quite simple phrases and, of course clever use of .... timing.
And lots of repetition. quite a lot of repetition. and then some more repetition (slightly changed of course).
Then you get three impassioned vocal verses - with call and response guitar fills - and then he rips out one final guitar chorus, incredibly intense, because it finally feels like he's holding nothing back.
Breaking it down crudely, then, it's basically a mix of:
1. quantity of notes - starting few, building to many;
2. dynamics - starting quiet, getting louder;
3. pitch register - starting low, getting higher
Of course, it's not a smooth gradient with any of them (that would be too predictable), there can be ups and downs along the way; sometimes all 3 build, sometimes only one or two. But generally a peak in all 3 will be reached towards the end of the solo.
All of these have natural parallels with the human voice, which is how they work. If someone gabbles or talks loudly, they're obviously excited. Same if they talk at a higher pitch than usual. And if they scream long and high, something serious is going on! (So soloists will often save long high notes for the end of a solo, like a cry of triumph on reaching the top of the mountain.)
(And I don't suppose I need to draw any sexual analogies... I'm sure you can draw your own...

)
Buddy Guy is very good at pulling you in using lots of silence - you move to the edge of your seat, wondering what he's going to say next! (IOW, space gives the next phrase more impact.) And he can focus on a single note, and chew on it like a dog with a bone. (Listen to the 20 seconds from 1:14 - Ow! And then the simple little repeated phrase after that.) In that case, it's the timing shifts, the stretching of note values, that contribute most suspense.
Here's one of the all-time classic jazz solos:
A Famous Solo by Paul Gonsalves - YouTube
This works rather differently. It's less in your face, and creeps up on you more. A lot of it is down to the swing groove the band has established, and the interaction of the
audience is critical.
But it's a great example of how excitement can be built by sheer repetition.
After a short solo by Elington himself, minimal and rhythmic, Gonsalves begins at 3:47.
For some time, it's nothing remarkable, just a cool swing groove. And none of the sax playing is especially adventurous. It's the relentlessness of it that starts to hook you in. And of course the growing ambience of claps, "yeah"s and whistles. This is just what jazz was always about. Not the intellectual artistic intensity of a Coltrane, but this infectious semi-delirium between band and audience together. Jazz was never supposed to be stuff you sat and stroked your chin to. IOW, this 1956 performance is harking back to when jazz was
pop music - dance music.
Jazz is very rarely (if ever) like this today, but blues (in the right hands) sometimes gets there, as does funk and hip-hop. A great solo is rootless (a private contemplation) without a great band behind it, kicking the soloist in the ass now and then.
In Buddy Guy's track, the band just backs him respectfully, but you can tell he's taking the crowd with him. IOW, that really is a solo "blues" performance, rather than a "jazz" one. And it has popular appeal because the language is simple and direct (no fancy scales or reharmonizations).
"Jazz", IMO - aside from things like fancy harmonies - implies a degree of
group improvisation: during one musician's solo, the band will be interjecting; the soloist may conduct them to some extent (eg bringing dynamics down), but they "talk back" to him too.