There are two kinds of Jenkins releases: LTS Release and Weekly Release. The Jenkins Weekly Release contains new features and bug fixes, whereas the LTS (Long Term Support) Release are special releases that are considered stable over a period of 12 weeks. It's recommended that you always choose an LTS Release for your Jenkins server:
Jenkins download page
Jenkins by itself notifies you when there is a newer version available (provided your Jenkins server has access to the internet), as shown in the following screenshot:
Jenkins notification about the availability of a new version