Day

day = on the (i.e. this) day (or night current or just passed)
1] this (very) day)
2] what has happened today
derivation: neuter (as adverb) of a presumed compound of the art. (3588) and (2250)
http://bible1.crosswalk.com/Lexicons/Greek/grk.cgi?number=4594&version=kjv

(3588)
this, that, these, etc.
http://bible1.crosswalk.com/Lexicons/Greek/grk.cgi?number=3588&version=kjv

(2250)
1] the day, used of the natural day, or the interval between sunrise and sunset, as distinguished from and contrasted with the night
   1.a] in the daytime
   1.b] metaph., "the day" is regarded as the time for abstaining from indulgence, vice, crime, because acts of the sort are perpetrated at night and in darkness
2] of the civil day, or the space of twenty four hours (thus including the night)
   2.a] Eastern usage of this term differs from our western usage. Any part of a day is counted as a whole day, hence the expression "three days and three nights" does not mean literally three whole days, but at least one whole day plus part of two other days.
3] of the last day of this present age, the day Christ will return from heaven, raise the dead, hold the final judgment, and perfect his kingdom
4] used of time in general, i.e. the days of his life.
derivation: from (with (5610) implied) of a derivative of hemai (to sit, akin to the base of (1476)) meaning tame, i.e. gentle
http://bible1.crosswalk.com/Lexicons/Greek/grk.cgi?number=2250&version=kjv

(5610)
1] a certain definite time or season fixed by natural law and returning with the revolving year
   1.a] of the seasons of the year, spring, summer, autumn, winter
2] the daytime (bounded by the rising and setting of the sun), a day
3] a twelfth part of the day-time, an hour, (the twelve hours of the day are reckoned from the rising to the setting of the sun)
4] any definite time, point of time, moment
derivation: apparently a primary word
http://bible1.crosswalk.com/Lexicons/Greek/grk.cgi?number=5610&version=kjv

(1476)
1] sitting, sedentary
2] firm, immovable, steadfast
derivation: from a derivative of hezomai (to sit)
http://bible1.crosswalk.com/Lexicons/Greek/grk.cgi?number=1476&version=kjv

The differences between the Jewish and Roman days:
The Jewish way of measuring and counting days is different than the Roman way. One difference is that a Jewish day begins at sundown. The Jewish day therefore begins approximately six hours before the Roman day. Another difference is that when counting elapsed days in the Jewish way, any fraction of a day (nighttime, daytime, or fraction of either) is counted as a full and completely elapsed day.

The "Day of Preparation" as an example:
The Jewish week has seven days, as does the Roman week. The Jewish week begins on Sunday, as does the Roman week. The sixth day of the Jewish week is called the "Day of Preparation". As mentioned above, the Jewish day starts six hours before the Roman day. The Day of Preparation, the sixth day of the Jewish week, therefore starts at sundown on the Roman Thursday, the fifth day of the Roman week.

What is being prepared for?
The preparation is for the Jewish "Sabbath" (the seventh day of the Jewish week) which is a holy day on which the Shewbread is offered. The Shewbread is offered at the beginning of the Sabbath which begins, as mentioned, at sundown on the Roman Friday, the sixth day of the Roman week.

How are elapsed days counted?
As an example, from noon on Monday to noon on Wednesday would typically be counted as three elapsed days in the Jewish way, despite the fact that merely 48 hours had elapsed instead of  72 hours. The reason for this seeming aberration is that the Jewish day begins at sundown instead of at midnight, as it does in the Roman way. So, although merely 1/4th of Monday remains at noon on Monday, and merely 3/4ths of Wednesday is gone by noon on Wednesday, the Jewish way counts Monday, Tuesday and Wednesday as having elapsed in this example. This example emphasizes that the Jewish way of counting elapsed days counts a day as elapsed even if less than half the day (or daytime or nighttime) had elapsed by counting hours on a clock. This fact is further emphasized by this additional example: from a minute after noon on Monday to 12:01 AM (merely a minute after midnight, just after Wednesday begins in the Roman way) would also be counted in the Jewish way as three elapsed days although merely 36 hours (1/4th of Monday, all of Tuesday, and 1/4th of Wednesday in the Jewish way) had elapsed on the clock.

What is the relevancy of all this?
One relevancy of this is seen in the counting of days that the Holy Spirit spent in Hell.