Strings come in ranges, measured in inches. Ernie Ball Regular Slinkys are 0.010 to 0.046 inches, high E to low E. The significant string is the thinnest, corresponding to the highest note. In this case, these are called "tens".
Jazz players and Stevie Ray Vaughn play with thicker strings, believing the greater mass gives the pickups more to get signal from. They hurt most players fingers, especially if they do something as foolish as try to bend them in standard tuning. Thrash metal players tune down from standard tuning, and the heavier strings make up for the slackness. This range starts at .011 and goes up from there, and we'll say that these are "Papa Bear" strings, too heavy for most uses.
Big bender types, like B.B. King, Billy Gibbons of ZZ Top, crazy bending country players, and the guitarist who writes this blog, go for thinner strings because they bend like butter, and if you want more signal, you can always turn up the amp or something, but they require self-control, so you only bend when you want to and don't bend/tighten until they break. This range starts at .008s, and is "Mama Bear" territory.
Somewhere between is the "just right", where you can bend what you want, but the strings are tight enough to not bend accidentally, where they don't hurt you, but you don't wreck them when tuning up or something. For some, it's .010s ("tens"), for some it's .009 ("nines"). Some makers even have a .0095 set. This is "Baby Bear", and since some guitars with tremolo systems are very hard to set up after string gauge changes, players get adamant. (Teles like mine are easy and forgiving in this regard.)
The same ideas are true for acoustic guitar, but since there's actual physics of making audible sound involved, and most acoustic players don't bend strings, the "Baby Bear" range is more like .011-.012 for the high string.
If you are an inexperienced guitarist: I suggest you go with tens, until you can express a reason related to your playing. Not "This guitarist plays heavy strings", but "I can't get the bends I need" or the like. If your fingertips hurt, you're squeezing too hard, which is pulling you out of tune, making your changes slower, and hurting your fingers. There is no good in it, and you're far better off getting your fingering together before you start playing around with other string gauges.
If you are shopping for a guitarist but know very little about guitar: This is not the place to guess. Ask them. They will tell you what they play, in greater detail than you really want. If they play with a tremolo system — if they have a strange metal arm sticking out of their guitar — there is a balance between strings and springs that needs to stay constant, or else they need to spend hours with screwdrivers and hex keys and tuners getting it back. The player in your life will tell you the gauges, the brand, the product line, and, if you get it wrong, it's like giving a fruitcake, socks, or an ugly Christmas sweater: they'll try to smile to be polite, but inside, they're groaning.
