This is the point where a particular deal leaves you with no overall profit or loss once all costs are factored in.
So if for example you buy a share for £2.50 and pay costs and commission of 5p, your breakeven point is £2.55 since at that price you could sell the share and recover all your costs (ignoring selling costs). If you buy a call option your breakeven point is the fixed strike plus any premium paid plus costs. With a put option it is the strike price minus any premium paid. So for example if a call option has a strike price of £2.50 and you have paid a premium of 20p per share with transaction costs of 5p per share the underlying share price will need to hit £2.75 (£2.50 + 20p + 5p) before you breakeven by exercising the option.