Assalamualaikum all ......
Salam Maal Hijrah 1436.
That's the wish that you heard many said. Some follows with apologizing for all the wrongdoings. And some with new determination and hopes. All are good. Nothing is wrong with that.
1. Good wishes - yes, we are encouraged to wish everybody good at any times, be it to someone that we know or we don't. The simplest and easiest way to say the wish is the simple 'Assalamualaikum warahmatullah'.
2. Apologize - yes, we are also required to always apologize for whatever wrongdoings that we might have done. Psychologically, the famous Dr Fadzilah Kamsah once said that everybody should practice to forgive people before going to bed everynight. It gives a pleasure feeling. If we apologize and able to forgive, we would be happier.
3. Determination and hopes - yes, we should always determine and hope to improve ourself day by day. As the saying, "Hopefully today is a better day than yesterday".
Hijrah is the Islamic calendar. It is devised during caliphate Osman ibnu Affan RA. It is not based on certain Islamic teaching. The months in arabic has already being known long during the jahiliah period. During the his time Saidina Osman thought that it is time when it is being recorded. Having a calendar. And he began marking the calendar during the month of Muharram. And in conjunction with the Prophet hijrah from Makkah to Madinah earlier, they called it the hijrah years. History recorded that the Prophet Muhammad SAW began his hijrah on 28th Safar and reach Madinah on 12 Rabiul Awwal. Therefore, 1st Muharram does not mark the day Prophet Muhammad's hijrah from Makkah to Madinah. 1st Muharam does not mark the day when your 'record book' is being brought to Allah SWT. There is no such thing as 'open book' or 'close book'.
The only thing that is relevant about Muharam to islamic teaching is the fasting on the 10th of Muharram. History recorded that there are many things happened on that day among which is the drowning of the Firaun in the Red Sea while going after Prophet Musa AS. And the fasting on the 10th of Muharram was earlier a compulsory on all Muslim before we are all instructed to fast throughout Ramadhan through the verse 183: alBaqarah. After the verse came, the fasting on the 10th of Muharram became a sunnah.
Just the year before the Prophet leaves the world, he got to know that the Jews were also fasting on the 10th of Muharram. He asked them and was told that it was a rememberance for the day Prophet Musa AS escapes and the drowning of Firaun, Prophet Muhammad claimed that Islam has a better right to appreciate that event. He later said, in a form of accepted Hadith that if he would live for another Muharram, he would perform the sunat fast (saum) on both the 9th and 10th of Muharram. This is to differentiate from the Jews' practice. However... the Prophet never had the opportunity to live for another Muharram. He passed away. And the sahabah claimed that based on his saying (hadith), we can perform the fast either on both 9 and 10th of Muharram.. or.. we only fast on the 10th. If the Muharram fasting was once a compulsory, it shows the high degree of importance for us to fast on that day.
So, lets do not miss this opportunity. As much as we want to be a better person in iman and taqwa, lets make this small step for a betterment... lets fast the Muharram fast. Whether to do it only on the 10th ot do it on both 9 and 10th. You know yourself to make a decision. But a decision not to fast is not acceptable at all.