Being responsive to emails is an easy way to show people that you value professional relationships and their time. We all get busy, but it's important to always show courtesy to the individuals who are taking time to reach out to you about anything.
Emails are an effective form of communication when used properly. If you see an email that requires more time than you have in the moment, respond to the sender to let them know you received the email then commit to a time when you can get back to them.
For some people, it's helpful to carve out time in each workday to just focus on creating and responding to emails. Many people focus on emails at the beginning or end of the day. Find a system that works for you and be sure you're following up to emails you get within 24-48 hours. Also be sure to use an out of office auto-response when you are away from the office or from emails for an extended period of time.
Other quick tips regarding emails are:
Keep your tone professional
Use a subject line that's specific, but short
Use proper email punctuation and good grammar
Always use greetings and salutations
Double-check your recipient's name
Make sure you know when to use "reply" vs. "reply all"
A little effort goes a long way when it comes to quality email communication.