Google shows in SERP snippet texts, which Google means are best describing your site. The only thing with which you could try to influence the SERP snippet content, is to write good meta description. But there is no warranty, that Google will indeed make use of it.
On the other side, there are not exact times known, after which Google shows the updated text on your site. If you have updated some things on your site, and Google still shows the old content, submit the content of the page to index,. like @closetnoc even recommended. And become sure, that the page you submit, isn't blocked against crawling/indexing and responses with nothing other but 200.
It could happen, that the updated text is placed dynamically by any kind of AJAx/JS etc. which could be closed against crawling - in this case Google will not show the updated text too.
it would be helpful to see a site to get to know about issues preventing new text appear in SERP snippet.