The difference between APPROACH minimums, and ALTERNATE minimums:
APPROACH minimums are stated on each approach plate, for instance, 200 ft. ceiling with 3 mi. visibility. It's a real-time minimum, because it only affects whether or not you can begin that particular instrument approach. On arrival, you check the airport's weather (METAR, for instance) and if the real weather is reported better than the required weather for a particular approach, then you can begin that approach. Therefore, you need to take the destination weather forecast into account when planning.
ALTERNATE minimums affect your PLAN, even BEFORE you take off, and is not related to approach minimums. An "alternate" refers to a second airport you identify in your planning that you can go to if the weather at the destination turns too bad to land. The thinking is that, if the weather at the destination is FORECASTED to be good around your arrival time (an hour before til an hour after), then you shouldn't need to list an alternate airport in your flight plan. Generally, the destination's weather has to be FORECASTED more than 2,000 ft. ceilings and 3 miles visibility, or if not, you have to IDENTIFY an alternate destination airport in your flight plan. The FORECASTED weather at the ALTERNATE airport has to be better than a certain ceiling / visibility, too. You have to look at the approaches available at the alternate to know what the minimum requirements are there. If the alternate airport has a "precision" approach (for instance, an ILS), the FORECASTED weather at the ALTERNATE has to be at least 600 ft. ceiling and at least 2 mi visibility, otherwise you can't list it as an alternate. But airports with a non-precision approach (for example, a VOR-A approach) require better conditions with 800 ft. ceilings.