An impediment or something that would cause problems; often used in polite expressions like 'if it's not inconvenient'.
差し支えなければ、お名前を教えていただけますか。
If it's not inconvenient, could you tell me your name?
その予定と差し支えがなければ、来週の会議に参加します。
If that doesn't conflict with your schedule, I'll attend next week's meeting.
差し支えがある場合は遠慮なくお知らせください。
If there is any problem, please let us know without hesitation.