on the contrary; rather; all the more
かえって expresses that an outcome is the opposite of what was expected, often with a sense of 'rather' or 'all the more'.
かえって indicates that the result is contrary to what was intended or expected. It often implies that an action meant to achieve one thing ends up causing the opposite effect. For example, if you hurry to catch a train and trip, you become later than if you had walked calmly. かえって highlights this ironic reversal.
It can also mean 'all the more' when something increases due to an action meant to reduce it. For instance, trying to hide a mistake might make it more noticeable. The nuance is that the result is worse or more intense than before, and there's a slight sense of regret or surprise.
In conversation, かえって is common and neutral, but it often appears in explanatory contexts. It can be used with both positive and negative outcomes, but the emphasis is on the contrast with expectation. It is not overly formal, so it fits in everyday speech as well as writing.