Firms have to be competitive in order to keep profits up and to remain in business. If they didn’t keep prices low then other firms could enter the market and undercut the incumbent firm, thus taking away its market share and supernormal profit. Alternatively rivals may do the same. These low prices benefit consumers and should result in more consumer surplus. Because prices are lower more of the good is demanded and hence the firm will produce more, this reduces allocative inefficiency as more resources are going towards the production of goods and services demanded by consumers (a definition of allocative efficiency).
In order to offer lower prices and prevent new entry (and hence a loss of market share and ultimately supernormal profits) firms have to be operating at X-efficiency (on their LRAC curve) and have to be productively efficient. Also by doing this (keeping costs as low as possible they may be able to increase their supernormal profits without having to raise prices and thus lose demand.
More competition means there are more firms in the market providing differentiated products. Firms will have to invest in designing and creating new innovative products in order to keep up with their rivals and to please consumers. By investing in research and development firms may also be able to patent goods, giving them an effective monopoly on that good, this acts as a further incentive for them to invest (so competition may result in increased R&D but in the long run the effect of this may be to create a monopoly which results in less competition). A wider range of choice is better for consumers, however this may reduce the productive efficiency of a firm as it wont be able to reap economies of scale due to the low quantity it will be producing (as there is likely to be many firms offering differentiated products). However this is assuming that competition only occurs when there are lots of firms in a market, this isn’t always the case, and there could be a lot of competition in a duopoly (2 firm) market. In this case there may be differentiated products but also the ability to gain economies of scale and hence produce productively efficiently (as well as being able to offer a lower price, or absorb a greater supernormal profit).
Another by-product of competition may be to improve quality. Firms will always be looking to outdo their rivals and one way they could do this is through improving the quality of their good in order to make their demand curve more inelastic (firms want to have an inelastic demand curve so that they can charge a higher price without seeing a fall in demand). In order to improve quality firms may invest in R&D.
The reasons above show why competition can be a good thing for society (in terms of efficiencies) and for consumers (lower prices, more products and better quality).