JIRA Connect allows you to use JIRA on a iOS and Android mobile device. JIRA Connect is available in multiple versions, not all features are available in all versions.
This documentation provides an overview of the enterprise functionality. Android and iOS functionality is mostly equivalent.
JIRA Connect Enterprise (requires Mobility for JIRA add-on)
JIRA Connect Professional for Android
JIRA Connect Enterprise for Android (requires Mobility for JIRA add-on)