Some investors will buy the property, and offer the tenants money to leave. This is called cash-for-keys.
Lets say a tenant is paying $1000 a month, but the unit could be getting $2000 a month. An owner negotiates to pay $20,000 to the tenant to leave, then rents it for $2000. This is an gross increase of $12,000 a year. 12,000/20,000 = 60% Cash on Cash return.
Some Investors will also look at the cap rate of the building. Lets run those numbers. Investors will assume anywhere between 30%-40% expenses. Lets use 30%. So 12K*.7= $8,400. Lets see how much value this adds to the building at a 6 cap: 8,400/.06= $140,000. 7 cap? 8,400/.07=$120,000
This is a bit over simplified as its really not looking at remodel work you'd likely want to do and other expenses, but I'm illustrating why investors care about upside in rents. The building becomes worth more when you increase rents.
Obviously deals where you can double rent are hard to come by. You really have to know the market the building is in, what you can get for that unit, and have plenty of cash. You also have to be comfortable with the risk that the tenant could say FU I want 100K...
That said, I could care less what a listing agent thinks about what the unit could rent for. Do your due diligence. You should generally know this rental market already to get to a ballpark, but run comps in the area. Craigslist, HotPads, WSR, etc.