I understand when there is tab that says:

7 8
and it's linked together by that bendy sign. You just hammer on from the seveneth fret to the eighth.

But what does it mean when there are several numbers linked by the bendy sign.?

And the hammer on sign is underneath all four?
It means you use all four of your fingers to hammer 1-2-3-4

Try playing 5-7-9 on the E, A, and D strings, using your index, middle and pinky fingers.
Well typically the 'bendy sign' means legato and not hammer on. Legato means to play all the notes in a smooth transition.

I was going to link you the first video I saw when i searched legato but I figured that is not worth your time. I'm sure there are posts on this forum about it and explain it well. (sorry I couldn't help you find them)
okay...so if a tab has 7h9h10, what that means is so play the first note by picking it.Then you hammer on to the note on the 9th fret and the note on the 10th fret. effectively what you're doing is both speeding up and smoothing out you're playing by replacing struck notes with hammer ons. Simply put struck notes take longer to execute, use of the hammer ons provides speed.
music is the only protection from the woes of the world; a citadel it shall stand evermore