The memory of an oscilloscope is the amount of data that it can store and display. The more memory an oscilloscope has, the longer and more detailed the waveform it can show. The memory also affects the sampling rate, as the oscilloscope may have to reduce the sampling rate to fit the data in the memory. Some oscilloscopes have adjustable memory depth, which allows you to optimize the trade-off between sampling rate and waveform length. The features of an oscilloscope are the functions and capabilities that it offers, such as triggering, decoding, math, measurements, cursors, and waveform analysis. These features can help you perform various tasks and tests on your circuit, such as measuring frequency, phase, amplitude, distortion, jitter, and more. You should choose an oscilloscope with the features that suit your application and preferences.