In non-denominational Christian teachings, 'sabbath' (Hebrew) means simply "to rest".
Christ became our Sabbath... we take comfort in Him and we rest in His Word. Every day is our 'sabbath' in Christ.
Some denominations have actually taken a less than correct interpretation of the word to assign a worship day of the week. While that is better than nothing, it does not fall into the proper usage of the word 'sabbath' as it applies to Christ becoming our 'rest'.
Hebrews 4:1-13 (KJV) mentions this in detail.
A full study can be found at the link below fo anyone who wishes to read about it from a non-denominational viewpoint.
Sabbath Bible Study