More than getting direct traffic from the directories, you can expect an improvement in the search engine rankings for your site. When search engines find your links in the directories, they measure the relevancy of these links and classify your website based on the anchor texts/titles you have used in your submissions. Getting such targeted links can, to a certain extent, help in improving your search rankings for those target terms (titles). Higher search engine rankings will consequently lead to an increase in incoming traffic to your site.
It could take anywhere between 3-90 days before your directory links are approved. On an average it has been seen that a site gets around 30-35% link approvals over a period of 90 days after the submissions have been made, since not all sites that are submitted, are necessarily reviewed by every directory.
While directory links do add value to your website, you should also continue your link building efforts through other means as well, such as getting linking from those sites that are related to yours or are similar in theme. Avoid building links with those sites which are of poor quality and do not have much subject matter. The links that you receive from relevant, high quality, well-structured sites with plenty of well-written content are most valued by search engines and these combined with directory links will give you a much better chance of ranking higher.