This is the 188th most frequent Spanish word.
mejorar
To improve.
In this sentence, 'mejorar' is an infinitive verb meaning 'to improve'. It is used to express a desire to enhance a skill in a specific area, that is, playing the piano.
Quiero mejorar mi habilidad para tocar el piano.
I want to improve my ability to play the piano.
Here, 'mejorará' is a conjugated form of 'mejorar' in the future tense, indicating a prediction that a condition (the weather) will become better in the upcoming time.
El clima mejorará mañana según el pronóstico.
The weather will improve tomorrow according to the forecast.
In this context, 'mejorar' is the infinitive form used to denote the action of making positive changes to enhance interpersonal relations.