As TNK and gman have already explained, when a reel is loaded with 2 types of line, the term "topshot" refers to the outer piece of line--the piece closer to the hook. The term came to be used when anglers began base-loading their reels with braided dyneema or spectra lines. This is usually done to get various benefits of the new, braided lines: (1) more spool capacity [because the braid is stronger at even smaller diameter than mono]; (2) stronger line [same reason]; (3) lighter weight and less drag [for same reason] vs wt and drag of an equal length of mono line allows smaller live baits [sardines] to perform better longer; (4) less stretch than mono [anglers claim they can feel the fish breathe on their bait]; (5) despite its initial cost, braid may be cheaper to maintain [braids are reported to have lasted for 10-12 yrs so far w/o losing strength, suppleness, whereas mono should be discarded regularly, sometimes after a day of fishing b/c of abrasion, stretch, sunlight exposure, etc.]; (6) hollow braids can be spliced at 100% strength, allowing bad [frayed, tangled, discolored, damaged] sections to be removed and good line returned to use w/o knotting the line. There's more, but I think those are the main reasons.
If the braid's so great, why use a topshot? Here are some comon reasons: (1) mono can be more stealthy and fluorocarbon may offer even more stealth, (2) mono sinks better, (3) mono offers shock absorption you may want if you can't get the shock absorption you want from your rod tip or avoid the need for it by backing off the drag; (4) mono is generally more abrasion resistant than braid--many anglers use 10-25 yd mono topshots to take the potential rubs against the hull as a green fish is brought near the boat; (5) using easily removable/changeable topshots allows more fishing flexibility on the water--a quick change from one line class to another; (6) easier to carry multiple topshots ready to use than to carry more reels or more spools of line.
Do you HAVE to use a topshot? No, certainly not for hardheads; but, I don't know experienced fisherman who uses braid w/o a topshot for important fishing (as opposed to just say just catching perch or blackfin because he can or because he needs bait).