This verse describes a specific step in the priestly ordination ceremony performed by Aaron, the first High Priest of Israel, after the Tabernacle was erected. Let's break it down:

"He presented the meal offering...": "He" refers to Aaron. The "meal offering" (also called a grain offering) was a sacrifice made of fine flour, oil, and frankincense. It was often offered alongside other sacrifices, like the burnt offering. It symbolized thanksgiving and dedication to God.

"...and filled his hand from there...": Aaron took a portion of the prepared meal offering (flour mixture) and filled his hand with it.

"...and burned it upon the altar...": He placed the handful of meal offering onto the altar fire, where it was burned as a sweet-smelling aroma to the Lord. This act symbolized a sweet savor offering to God.

"...besides the burnt offering of the morning.": This indicates that the meal offering was burned in addition to the regular burnt offering that was offered every morning. This reinforces the idea that this day was a special, comprehensive day of dedication and consecration.

In summary: This verse describes Aaron offering a meal offering (a grain-based offering) by taking a handful and burning it on the altar. This was done alongside the regular morning burnt offering, indicating a special and complete act of worship and dedication.

Significance:

Part of a Dedication Ritual: This was part of a larger ritual to consecrate Aaron and his sons as priests and to dedicate the Tabernacle for use.
Specific Act of Worship: The meal offering was a particular form of worship, representing thanksgiving, dedication, and dependence on God for sustenance.
Order and Precision: The verse shows the prescribed order of the sacrifices, highlighting the importance of following God's instructions precisely.
Foundation of Priestly Service: This event marked the beginning of the Levitical priesthood and the formal sacrificial system in Israel.