Hydraulic tappets use oil pressure to maintain a "zero" clearance between the cam and the valve.

If you use sustained high revs or very high lift cams you can run in to problems with the hydraulic tappets sticking open.

Solid tappets bacially are shims and bucket tappets that replace your hydraulic tappets. The downside is you need to manualy adjust your tappets at fairly regular intervals (like 10k miles).

Alex