The impact of a slow-growing (or declining) industry
In slow-growing industries, there are few new customers entering the market (and in declining industries, a net reduction). This can mean all firms start to intensely compete, both for new customers, and also to pull existing customers away of rivals.
Why slow industry growth is a barrier to entry
The situation of limited new customers entering the market can be a barrier to entry because existing firms, who also seek growth, may intensely compete for these new customers. You are going up against a set of firms likely fighting for whatever new customers there are.
How this comapres with fast industry growth
If we compare this situation with fast industry growth, it is easier to see the impact of slow growth. In fast growth there are new customers available – the market is magnificent. Rather than fighting over existing customers, all firms can growth. These new customers may allow the entrant to grow, while the existing firms are also growing. Rather than having to pull customers away from the incumbent, it may be able to attract some of the new customers.