Robione,
TBO, represents the manufacturers estimate of an average time between overhauls. It's not a limitation except for commercial operations. An engine may or may not make TBO...it may require overhaul sooner, or it may go far beyond TBO.
An airplane operating privately, in other words not in commercial operations, may be operated "on condition." That means that so long as the engine is in acceptable condition and no life-limitations have been exceeded, the engine may continue to be operated.
TBO really only applies to the first run of the engine...when it's factory fresh, before the first "overhaul." The number applies to subsequent overhauls, but it's premised on starting with all new parts with all new tolerances and clearances met...a factory engine. When an engine is overhauled, it's seldom done by the manufacturer, and very often many components are left in the engine...so long as they're within specification, they may remain in the engine unless they're a life limited component. "Overhaul" means nothing more than the engine has been inspected and found to be in tolerance. Point is...it may not last nearly what the published TBO is.
Bear in mind that expensive accessories such as the magnetos are going to require service before TBO expires...you will go about 600 hours max on a set of mags before they need servicing and overhaul...to engine TBO certainly doesn't show the full picture. Consider the propeller, too...especially a constant speed prop. It's going to have it's own TBO and limitations.
On compression checks; these don't mean a whole lot. A compression check will show different numbers if checked twice in a row, or with two different test sets, or by two different people. Much like blood pressure, it's a tool to look at the life of the engine over a series of checks, as a trend. It's also a spot inspection tool to trouble shoot specific problems (such as a leaking valve)...but the lay person tends to put far too much stock in compression tests. Additionally, the numbers can be artificially bumped up during a pre-sale inspection to make the compression seem higher than it really is. Don't base your decisions around the compression, unless it's unusually low.
The operational history of the airplane is important...look at how often it's been flown, and how. An airplane that gets flown once every six months may not make TBO...sitting is hard on airplanes and equipment...regular operation is benificial to the health of the engine and airplane. Look at the logbooks to see what's been done in the past. A history of multiple cylinder changes, for example, shows that the airplane has probably been abused, and that the maintenance may have been subpar. Check that airworthiness directives have ben accomplished...an engine lacking the updated VAR crankshaft, for example...could become very expensive for you after the fact.
Get a mechanic ("engineer") you trust and invest in a thorough pre-buy inspection. Don't count on getting the full TBO life out of the engine. You may, or you may not, but certainly don't count on it if it's not the first run of the engine. If it's already been overhauled, you may get another good run on that engine...or it may require expensive servicing long before. Be prepared for that. Ask for the oil analysis history if there is one, and get a spectrometric oil analysis done. Good luck.