Memory leaks in Android applications can lead to slow performance and issues with features like Android Studio's Instant Run, as they occur when unused objects are not recognized and removed by Java's garbage collector. Detecting and resolving these leaks involves using tools such as Android Studio's Memory Monitor, which helps track memory allocation and identify leaks through heap snapshots, and Leak Canary, a library by Square that notifies developers of leaks without needing a continuous connection to Android Studio. Additionally, Facebook's Infer, a static analysis tool, aids in identifying potential resource leaks and other bugs, and can be integrated into continuous integration processes to enhance code quality. These methods collectively help maintain efficient memory usage and app performance.