As explained in the comments best bid and best offer (best ask) are the best prices at which you can respectively sell and buy at least one unit of the asset your are considering.
When backtesting a strategy, most people usually either use best bid and best offer or even worse last price.
The problem is that these prices are only available for a limited amount of units. Therefore if you start trading a substantive amount of lots, you might not have enough liquidity in the market (i.e. enough units available at best bid/offer), and you would then trade at a prices which is not as good as the one provided by the best bid/offer. This is all part of the implementation shortfall.
So, if you use best bid/offer prices for your backtest, you have to keep in mind that the result you get did not take into account the size of your trades and hence that the results are only significant for a small size; you always assume full liquidity and hence the best price possible for each and every trade. This is not a very realistic scenario, even more when you consider that the smaller the size, the larger the transaction costs in relative terms.
In general, you should first perform your backtest using best price/offer to see if your strategy is profitable in the best scenario. If you're happy with that, you can carry on taking into account the market depth (bid and ask beyond the best) and transaction costs. Anyway, backtest is never perfect and you should expect that a live execution of the strategy would not perform the same, and most of the time not as well as in the simulation.