I make minimum wage at my company.  Do you feel that's fair?
Minimum wage isn't a lot of money, that's not fair. Exploitation of labour is the act of work being done for too little reward.
I think a lot of companies today like to pay too little for work.  Or hire overseas where they can pay less.
Yes that's true, local jobs are lost to overseas because of cheap labour. Cost of living is lower there that's the problem so they can work for less.
So is exploitation of labour when companies want to pay less than minimum wage for work?  I know that's illegal if they are a legitimate company.
Exploitation of labour is defined as treating ones employess unfairly for the owners benefit, it's basically when they can afford to pay you more but don't. It could still be the minimum wage rate.
For example, when the company I work for is all over the news bragging about their profits for the year, but they pay minimum wage.  They also increased ticket prices.
Yeah that's it, for instance if you were a small firm and wanted to hire an assistant and you were not making much turnover and you paid what you could afford then that's not exploitation, it's when firms knowingly pay less deliberately.
That makes sense!  Thanks for the example - that helps to understand exactly what it is.  
Yeah it's the unfair nature of it, it's when there's big fat cat shareholders creaming off the profits when the hamburger fryer is struggling to get by kinda thing.